document.write( "Question 593028: I need help!!\r
\n" ); document.write( "\n" ); document.write( "Find a polynomial with real coefficients that has zeros: 1, 4 + i, 4 – i \n" ); document.write( "

Algebra.Com's Answer #376164 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If

is a zero of a polynomial with real coefficients in

, then

is a factor of the polynomial. With that in mind:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "is the fully factored polynomial. All you need to do is multiply it out. Hint for less confusing algebra: Treat

and

as binomials with the complex number constants as single terms. Remember that the product of a conjugate pair of complex numbers is the SUM of two squares.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "John
\n" ); document.write( "

\n" ); document.write( "My calculator said it, I believe it, that settles it
\n" ); document.write( "

$\"The$

\n" ); document.write( " \n" ); document.write( "

\n" );